Regularity properties of viscosity solutions for fully nonlinear equations on the model of the anisotropic p→-Laplacian

Article type: Research Article

Authors: Demengel, Françoise

Affiliations: Laboratoire AGM, UMR 8088, University of Cergy Pontoise, France. E-mail: demengel@u-cergy.fr

Abstract: This paper is devoted to some Lipschitz estimates between sub- and super-solutions of Fully Nonlinear equations on the model of the anisotropic p→-Laplacian. In particular we derive from the results enclosed that the continuous viscosity solutions for the equation ∑1N∂i(∂iu|pi−2∂iu)=f are Lipschitz continuous when supipi<infipi+1, where p→=∑ipiei.

Keywords: Degenerate fully Nonlinear equations, p→ anisotropic Laplacian, viscosity solutions, regularity

DOI: 10.3233/ASY-171433

Journal: Asymptotic Analysis, vol. 105, no. 1-2, pp. 27-43, 2017